Goal understands Madrid reached an agreement with Monaco over an £70 million transfer fee over the weekend and finalised personal terms with the player and his representatives on Monday.
The European champions made the Colombia international their principle transfer target on the back of the 23-year-old's stellar performances for his country at this summer's World Cup in Brazil, with the attacking midfielder winning the Golden Boot after netting six times in just five games.
James will now be presented to the press and Madrid fans on Tuesday, with the construction of a special stage for the ceremony at the Bernabeu already well under way.
Meanwhile, the Liga outfit are also still hoping to persuade Monaco to part company with another Colombia international, Radamel Falcao.
Indeed, los Blancos have already made a breakthrough in their bid to bring the former Atletico attacker back to the Spanish capital, but the proposed transfer hinges upon Madrid's medical department declaring themselves satisfied with the striker's recovery from cruciate ligament surgery earlier this year.
The James deal is also likely to leave Isco surplus to requirements at the Santiago Bernabeu.
The Spain international only joined Los Blancos from Malaga last summer but, after struggling to nail down a regular berth in Carlo Ancelotti's starting line-up, could be offloaded, with Premier League outfit Liverpool closely monitoring the playmaker's current situation.